=100+2/(2²-1)+2/(3²-1)+2/(4²-1)+……+2/(100²-1)
=100+2/1×3+2/2×4+2/3×5+……+2/99×101
=100+2/1×3+2/3×5+……+2/99×101+2/2×4+2/4×6+……+2/98×100
=100+1/1-1/101+1/2-1/100
=101又9899/10100
2/1×3=(3-1)/1×3=1/1-1/3
其它类似